Methods are provided for designing and generating a tool path for three-dimensional printing of a fiber composite part. The method includes defining a three-dimensional domain model and determining a set of boundary conditions for the three-dimensional domain model. The methods include applying a gradient-based algorithm to a predetermined stress state located within the three-dimensional domain model in order to: (1) optimize the three-dimensional domain model for minimum deflection or stress using a structural mechanics algorithm for a composite article, and (2) provide a topologically optimized fiber composite part design and fiber orientation field. The methods include using the topologically optimized fiber composite part design and fiber orientation field as an input to solve gray-Scott reaction diffusion equations to generate an anisotropic tool path for three-dimensional printing of the fiber composite part.
|
15. A three-dimensional printed fiber composite article comprising:
at least one fiber reinforcement having a shape and size defining a three-dimensional domain space, the fiber reinforcement being disposed in the three-dimensional domain space in a predetermined pattern having a predetermined fiber direction and pitch path, wherein the predetermined pattern is based on an anisotropic tool path obtained by solving gray-Scott reaction-diffusion equations using an anisotropic diffusion tensor.
20. A method of generating a tool path for three-dimensional printing of a fiber composite part, the method comprising:
defining a three-dimensional domain model;
determining a set of boundary conditions for the three-dimensional domain model;
applying a gradient-based algorithm to a predetermined stress state located within the three-dimensional domain model in order to: (1) optimize the three-dimensional domain model for minimum deflection or stress using a structural mechanics algorithm for a composite article, and (2) provide a topologically optimized fiber composite part design and fiber orientation field; and
using the topologically optimized fiber composite part design and fiber orientation field as an input to solve reaction diffusion equations using an anisotropic diffusion tensor to generate an anisotropic tool path for three-dimensional printing of the fiber composite part.
1. A method of generating a tool path for three-dimensional printing of a fiber composite part, the method comprising:
defining a three-dimensional domain model;
determining a set of boundary conditions for the three-dimensional domain model;
applying a gradient-based algorithm to a predetermined stress state located within the three-dimensional domain model in order to: (1) optimize the three-dimensional domain model for minimum deflection or stress using a structural mechanics algorithm for a composite article, and (2) provide a topologically optimized fiber composite part design and fiber orientation field; and
using the topologically optimized fiber composite part design and fiber orientation field as an input to solve gray-Scott reaction diffusion equations using an anisotropic diffusion tensor to generate an anisotropic tool path for three-dimensional printing of the fiber composite part.
2. The method of generating a tool path according to
3. The method of generating a tool path according to
4. The method of generating a tool path according to
5. The method of generating a tool path according to
6. The method of generating a tool path according to
7. The method of generating a tool path according to
8. The method of generating a tool path according to
9. The method of generating a tool path according to
10. The method of generating a tool path according to
11. The method of generating a tool path according to
12. The method of generating a tool path according to
13. The method of generating a tool path according to
16. The three-dimensional printed fiber composite article of
17. The three-dimensional printed fiber composite article of
18. The three-dimensional printed fiber composite article of
19. The three-dimensional printed fiber composite article of
|
The present disclosure generally relates to methods for additive manufacturing and, more particularly, to methods for tailoring and customizing the generation of a tool path for printing a three-dimensional composite parts.
The background description provided herein is for the purpose of generally presenting the context of the disclosure. Work of the presently named inventors, to the extent it may be described in this background section, as well as aspects of the description that may not otherwise qualify as prior art at the time of filing, are neither expressly nor impliedly admitted as prior art against the present technology.
Tool paths may be used with additive manufacturing techniques to generate a pattern useful for the creation of an object. With additive manufacturing techniques that create anisotropic materials for reinforcement, such as continuous fiber printing (CFP) and tailored fiber placement (TFP), the tool path design may become more important in the structural integrity of the created object. In certain aspects, it is useful to have evenly pitched parallel paths with a width of the tooltip to fill the space. The conventional tool paths for CFP and TFP are based on geometrical information, and may be determined by manual design either by engineers or using design rules, such as a concentric rule (tool path is parallel to the outer perimeter) or isotropic (stacking of unidirectional oriented parallel pattern), or may be determined based on a structural analysis result. Alternatively, if one wants to achieve a fiber layout to follow a given vector field with anisotropic topology optimization, the tool paths are manually drawn in order to satisfy two main conditions. First, that there is an evenly pitched parallel space filling condition. Second, that the given orientation distribution is followed as much as possible. The manual optimization is both time consuming and costly. In certain automatic generation cases, conventional algorithms are based on stream line tracing of points that move along with a given direction, which is difficult to control a distance between paths.
Accordingly, it would be desirable to provide improved, cost effective, and automated methods of tool path generation that can be customized for various design considerations.
This section provides a general summary of the disclosure and is not a comprehensive disclosure of its full scope or all of its features.
In various aspects, the present teachings provide a method for designing and generating a tool path for three-dimensional printing of a fiber composite part. The method includes defining a three-dimensional domain model and determining a set of boundary conditions for the three-dimensional domain model. The methods include applying a gradient-based algorithm to a predetermined stress state located within the three-dimensional domain model in order to: (1) optimize the three-dimensional domain model for minimum deflection or stress using a structural mechanics algorithm for a composite article, and (2) provide a topologically optimized fiber composite part design and fiber orientation field. The methods include using the topologically optimized fiber composite part design and fiber orientation field as an input to solve Gray-Scott reaction diffusion equations to generate an anisotropic tool path for three-dimensional printing of the fiber composite part.
In other aspects, the present teachings provide a three-dimensional fiber composite part or article made in accordance with the methods described herein. In various aspects, the three-dimensional fiber composite article includes at least one fiber reinforcement having a shape and size defining a three-dimensional domain space. The fiber reinforcement is disposed in the three-dimensional domain space in a predetermined pattern having a predetermined fiber direction and pitch path. The predetermined pattern is based on an anisotropic tool path obtained by solving Gray-Scott reaction-diffusion equations. The predetermined pattern may have a variable pitch path that is based on one of a localized thickness of the fiber composite article, and a localized predetermined stress state of the fiber composite article.
Further areas of applicability and various methods of enhancing the above technology will become apparent from the description provided herein. The description and specific examples in this summary are intended for purposes of illustration only and are not intended to limit the scope of the present disclosure.
The present teachings will become more fully understood from the detailed description and the accompanying drawings, wherein:
It should be noted that the figures set forth herein are intended to exemplify the general characteristics of the methods, algorithms, and devices among those of the present technology, for the purpose of the description of certain aspects. These figures may not precisely reflect the characteristics of any given aspect and are not necessarily intended to define or limit specific embodiments within the scope of this technology. Further, certain aspects may incorporate features from a combination of figures.
Additive manufacturing is a technique used to create a three-dimensional component by aligning and/or depositing overlapping layers of materials under the guided control of a computerized or programmed device. The present technology generally teaches methods for optimizing the generation of a tool path useful for additive manufacturing of an article or part. In particular, the present technology pertains to the creation of a fiber composite component with fibers as the additive material.
Conventional tool paths are usually generated based solely on geometrical information alone. The desired tool path for additive manufacturing follows a given vector field for the three-dimensional printing. However, if one wants to achieve a fiber layout to follow a given vector field with anisotropic topology optimization, the paths are manually drawn in order to satisfy two main conditions. First, that there is an evenly pitched parallel space filling condition. Second, that the given orientation distribution is followed as much as possible. In this regard, the novel tool path of the present technology is generated based on a contour of a field value of modified Gray-Scott (GS) equations. In various aspects, the GS equations can generate a line and space pattern with an even pitch by providing an appropriate parameter set. For example, the line direction is affected by boundary and initial value, and the GS equation is then modified with a different diffusion tensor for more control of the tool path generation. In various aspects, components can be made using a fine tow carbon composite, for example, having a diameter or thickness of between about ¼ to about ⅛ inch. The fibers can be oriented throughout the domain space in conjunction with a stress scalar/tensor, for example, along principal stress directions, or along principal, secondary, tertiary, etc. directions, depending upon the nature of a stress and/or strain input model and von Mises yield criterion.
The use of the modified GS equation provides the distribution of an anisotropic diffusion tensor on its diffusion term, and the diffusion tensor is also time dependent. The path pitch can be defined by the value of the diffusion coefficient. In the modified GS equation, the second principal element of the diffusion tensor (i.e., the short axis of the diffusion tensor) is kept constant, but the first principal element is time dependent and is stretched out to be larger in the given direction. The amount of stretch is controlled by time. For example, by making it larger, the pattern becomes more directional, but at the same time, it becomes coarse because the diffusion value itself becomes larger in the given direction. To the contrary, if the diffusion tensor element in the first principal direction becomes smaller, ultimately the same value as the second principal direction, that is isotropic, the pattern becomes less directional. However, due to the nature of the original GS equation, the line direction depends on the initial, or previous state, and the pattern still keeps the given direction distribution. The methods of the present technology repeatedly solve the GS equations for some time period and switch the anisotropy strength using at least two sets of diffusion tensors. By respectively changing the amount of stretch by time, the line pattern becomes more continuous, follows well, and is well packed.
In various aspects, the present technology additionally provides a gradual path pitch distribution control. For example, in the case of additive manufacturing techniques using tailored fiber placement (TFP), the path generally determines the thickness of the product. Thus, the path pitch distribution control can be an important variable used to design a variable thickness product. With the present technology, changing the value of the diffusion coefficient by the thickness distribution generates a pattern for a variable thickness. In this regard, the relationship between the thickness and the diffusion coefficient is linear.
In addition to three-dimensional optimization where the fiber content is designed locally in three-dimensional space, the present technology is also applicable to two dimensionally optimized components. For example, in instances where full three-dimensional optimization is cost prohibitive with respect to the amount of computational time required, a two-dimensional composite part optimization may be performed. In this regard, the tailoring of the TFP path pitch spacing and product thickness may be logically linked to a stress magnitude, for example, a Von Mises stress, where tighter pitch spacing and thus final part thickness corresponds to higher levels of stress, and vice versa.
As will be described in more detail below, the extraction of the path from the GS equation results from obtaining a scalar field. The output pattern is a distribution of high scalar values and low scalar values, similar to monochrome image data where a high value is black, and a low value is gray. In certain aspects, the line pattern itself may contain many branches. However, it should be understood that branches are not desirable for the tool path because it would require extra movement to branch points, and extra starting points in the middle of the work area. The present technology uses a contour of the scalar field to generate a tool path, thus preferably generating a group of paths that do not have any branches.
In various aspects, methods for designing and generating a performance sensitive tool path for a composite fiber component first include defining boundary conditions and loads for an optimization domain. Certain methods may include performing an interpolation process. Many exemplary methods include using a gradient-based topology algorithm (MMA or GCMMA) looped in with a stress analysis, the domain is then optimized for minimum deflection (or minimum stress, depending on the objective) using the standard structural mechanics formulations for the composite media. Based on the topology optimized design and fiber orientation field, the GS equations are utilized to generate an anisotropic tool path for TFP or continuous fiber printing (CFP). The fiber spacing may be based on the desired final part thickness, printing constraints and the aforementioned design information.
To further understand the methods of the present technology,
Methods of designing a tool path for printing a three-dimensional fiber composite part may begin with defining a predetermined three-dimensional domain model of a fiber composite part along with a set of boundary conditions for the three-dimensional domain model. The methods may include defining a predetermined stress state within the three-dimensional domain model by applying a predetermined load to the three-dimensional domain model. A stress gradient-based algorithm may then be used to optimize the domain for minimum deflection (i.e., strain) or stress using a structural mechanics algorithm for a composite article.
The gradient-based algorithms are applied to a predetermined stress state located within the three-dimensional domain model in order to: (1) optimize the three-dimensional domain model for minimum deflection or stress using a structural mechanics algorithm for a composite article, and (2) provide a topologically optimized fiber composite part design and fiber orientation field.
Once obtained, the methods continue by using the topologically optimized fiber composite part design and fiber orientation field as an input to solve Gray-Scott reaction diffusion equations to generate an anisotropic tool path with a variable pitch for three-dimensional printing of the fiber composite part.
As is known in the art, reaction-diffusion systems are mathematical models that correspond to physical phenomena. In one example, a change in space and time of the concentration of one or more chemical substances is modeled. In mathematical terms, reaction-diffusion systems generally take the form of semi-linear parabolic partial differential equations represented by the general form as follows:
∂tq=D∇2q+R(q),
where q(x, t) represents the unknown vector function, D is a diagonal matrix of diffusion coefficients, and R accounts for all local reactions. Reaction and diffusion of chemical species can produce a variety of patterns, reminiscent of those often seen in nature. The Gray-Scott equations model such a reaction and are generally provided as follows:
The partial differential equations modeling this process may be simulated with a variety of numerical techniques. In various aspects, good results can be obtained using methods such as forward Euler integration of the finite-difference equations that one obtains by spatial discretization of the Laplacian, or the diffusion coefficients can be estimated for a target height field. For example, in various aspects the value of (pitch){circumflex over ( )}2 (i.e. one over the square of the height) can be used to approximate the diffusion coefficient. The pitch is inversely proportional to the height. A smaller pitch increases the density, providing the fibers closer to each other, which increases the height dimension.
The Gray-Scott reaction diffusion model is a mathematical model that describes the behavior of two chemical substances, and calculates the concentration of the two substances at a given time based upon the substances diffusion, feed rate, removal rate, and a reaction between the two. This simulation not only models the underlying process of a chemical reaction but can also result in patterns of the substances that are remarkably similar to patterns found in nature. Examples include patterns on animals, such as stripes on zebras, a leopard's skin, spots on butterflies, patterns on fish; fingerprints; ripples on sand; patterns of veins on a leaf; and various other biological phenomena. With the present technology, certain of the patterns resulting from this model can be used for the design of at least a portion of a fiber orientation angle distribution pattern.
To illustrate the model, one analogy presented is to imagine an area or space containing various concentrations of each chemical substance U and V at time zero. Over time, substance U is fed into the reaction at a given rate, while substance V is removed at a given rate.
Further, two molecules of V can react with one of U, which converts the substance of U to V as follows:
U+2V→3V
V→P
U, V, and P are chemical substances. A simulation is accomplished using the two partial differential equations listed above, each representing the change in concentration of a substance over time, where u and v are independent variables that represent their respective concentrations; Du and Dv are their respective diffusion rates or diffusion tensors, which can be calculated from permeability. The parameter k represents the rate of conversion of V to P; and F represents the rate of process that feeds U and drains U, V, and P. The parameters k and F are arbitrary positive numbers that can be adjusted. Each diffusion tensor is generally a 3×3 matrix reflecting diffusion rates in different directions.
The change in u (upper partial differential equation) is dependent upon its reaction with v (hence the subtraction (−) of uv2) and is fed at a certain rate (+F, scaled to its current concentration). The change in v (lower partial differential equation) is dependent upon its reaction with u (hence the addition (+) of uv2), and is removed at a given rate (−k, scaled by the feed rate and concentration of V). The concentration of U or V at each position is updated at each time increment (typically 1) based upon the result of the corresponding equation. The values for the feed rate, removal rate, and diffusion rate are entered into the equations. For example, on a 2D grid, the Laplacian Operator could be calculated on a convolution matrix. To calculate the new concentration, the current concentration and each surrounding concentration is multiplied by the corresponding value in the matrix (where the current position corresponds to the center position in the convolution matrix) and all values summed. This value technically represents the difference in concentrations between the current position and the surrounding positions.
The above model can be programmed in a suitable computer code as is known in the art. In various aspects, the resulting model provides an image representing the reaction container, with each point or pixel of the image representing the concentration of V (v) at that position. For example, the Gray-Scott reaction diffusion equations can be solved with various numerical methods, such as the finite differential method or the finite element method. The initial value of u and v could be random noise distribution. By solving the Gray-Scott equations for some time period with an appropriate parameter set, a steady state is obtained. Then, the contour line of the obtained structure is interpreted as a fiber deposition path. For instance, by tracing the contour line of the median value of the field, the line traces the perimeter of the black domain. The single stroke line is obtained for each isolated black domain.
In various aspects, the present technology may use the Gray-Scott reaction diffusion equations to obtain an anisotropic pattern layout. This may include using an anisotropic diffusion tensor with the Gray-Scott equations.
In various aspects, a weak and strong anisotropic tensor set is alternately used to obtain a connected line and space pattern, along with the given orientation field. The lateral direction defines the path pitch. With an isotropic diffusion tensor, the ratio of the path pitch (a) to the length (b) can be represented as a:b=1:1. For a weakly anisotropic tensor, the ratio of a:b is between about 1:1 to about 1:5. For a strongly anisotropic tensor, the ratio of a:b may be up to about 1:100. By stretching the tensor in the longitudinal direction, which is the fiber direction, the line and space pattern can be obtained. In various aspects, at least two sets of diffusion tensors are used to repeatedly solve the reaction diffusion equations: an isotropic or weakly anisotropic set, and a strongly isotropic set. In various methods, the Gray-Scott equations may be solved for some time period, where the diffusion tensor sets alternate in strength from weak to strong. For example, the diffusion tensor may be switched from isotropic→anisotropic→isotropic. This may be repeated several times, preferably finishing with either a weakly anisotropic set or completely isotropic set.
In various aspects, the method of generating a tool path includes repeatedly solving the Gray-Scott reaction diffusion equations for a time period and alternating between using weakly anisotropic and strongly anisotropic diffusion tensors. In one specific example, the methods include finishing the repeated solving of the Gray-Scott reaction diffusion equations with either a weakly anisotropic set of diffusion tensors or an isotropic set of diffusion tensors. In this regard,
The foregoing description is provided for purposes of illustration and description and is in no way intended to limit the disclosure, its application, or uses. It is not intended to be exhaustive or to limit the disclosure. Individual elements or features of a particular embodiment are generally not limited to that particular embodiment, but, where applicable, are interchangeable and can be used in a selected embodiment, even if not specifically shown or described. The same may also be varied in many ways. Such variations should not be regarded as a departure from the disclosure, and all such modifications are intended to be included within the scope of the disclosure.
As used herein, the phrase at least one of A, B, and C should be construed to mean a logical (A or B or C), using a non-exclusive logical “or.” It should be understood that the various steps within a method may be executed in different order without altering the principles of the present disclosure. Disclosure of ranges includes disclosure of all ranges and subdivided ranges within the entire range, including the endpoints.
The headings (such as “Background” and “Summary”) and sub-headings used herein are intended only for general organization of topics within the present disclosure, and are not intended to limit the disclosure of the technology or any aspect thereof. The recitation of multiple embodiments having stated features is not intended to exclude other embodiments having additional features, or other embodiments incorporating different combinations of the stated features.
As used herein, the terms “comprise” and “include” and their variants are intended to be non-limiting, such that recitation of items in succession or a list is not to the exclusion of other like items that may also be useful in the devices and methods of this technology. Similarly, the terms “can” and “may” and their variants are intended to be non-limiting, such that recitation that an embodiment can or may comprise certain elements or features does not exclude other embodiments of the present technology that do not contain those elements or features.
The broad teachings of the present disclosure can be implemented in a variety of forms. Therefore, while this disclosure includes particular examples, the true scope of the disclosure should not be so limited since other modifications will become apparent to the skilled practitioner upon a study of the specification and the following claims. Reference herein to one aspect, or various aspects means that a particular feature, structure, or characteristic described in connection with an embodiment or particular system is included in at least one embodiment or aspect. The appearances of the phrase “in one aspect” (or variations thereof) are not necessarily referring to the same aspect or embodiment. It should be also understood that the various method steps discussed herein do not have to be carried out in the same order as depicted, and not each method step is required in each aspect or embodiment.
Nomura, Tsuyoshi, Dede, Ercan Mehmet
Patent | Priority | Assignee | Title |
Patent | Priority | Assignee | Title |
9149988, | Mar 22 2013 | MARKFORGED, INC | Three dimensional printing |
9370896, | Jun 05 2013 | MARKFORGED, INC | Methods for fiber reinforced additive manufacturing |
9656429, | Aug 09 2016 | STRATASYS, INC | Systems and methods for structurally analyzing and printing parts |
9688028, | Mar 22 2013 | MARKFORGED, INC | Multilayer fiber reinforcement design for 3D printing |
9694544, | Mar 22 2013 | MARKFORGED, INC | Methods for fiber reinforced additive manufacturing |
9789652, | Feb 26 2014 | FREESPACE COMPOSITES INC ; ARMSTRONG, NATHAN | Manufacturing system using topology optimization design software, novel three-dimensional printing mechanisms and structural composite materials |
20090037148, | |||
20170173868, | |||
20170334136, | |||
20180065309, | |||
20180370145, | |||
20180372488, | |||
JP2019116104, |
Executed on | Assignor | Assignee | Conveyance | Frame | Reel | Doc |
Jul 26 2019 | NOMURA, TSUYOSHI | TOYOTA MOTOR ENGINEERING & MANUFACTURING NORTH AMERICA, INC | ASSIGNMENT OF ASSIGNORS INTEREST SEE DOCUMENT FOR DETAILS | 049970 | /0449 | |
Jul 26 2019 | DEDE, ERCAN M | TOYOTA MOTOR ENGINEERING & MANUFACTURING NORTH AMERICA, INC | ASSIGNMENT OF ASSIGNORS INTEREST SEE DOCUMENT FOR DETAILS | 049970 | /0449 | |
Jul 29 2019 | Toyota Motor Engineering & Manufacturing North America, Inc. | (assignment on the face of the patent) | / | |||
May 18 2021 | TOYOTA MOTOR ENGINEERING & MANUFACTURING NORTH AMERICA, INC | Kabushiki Kaisha Toyota Chuo Kenkyusho | ASSIGNMENT OF ASSIGNORS INTEREST SEE DOCUMENT FOR DETAILS | 056324 | /0760 |
Date | Maintenance Fee Events |
Jul 29 2019 | BIG: Entity status set to Undiscounted (note the period is included in the code). |
Date | Maintenance Schedule |
May 18 2024 | 4 years fee payment window open |
Nov 18 2024 | 6 months grace period start (w surcharge) |
May 18 2025 | patent expiry (for year 4) |
May 18 2027 | 2 years to revive unintentionally abandoned end. (for year 4) |
May 18 2028 | 8 years fee payment window open |
Nov 18 2028 | 6 months grace period start (w surcharge) |
May 18 2029 | patent expiry (for year 8) |
May 18 2031 | 2 years to revive unintentionally abandoned end. (for year 8) |
May 18 2032 | 12 years fee payment window open |
Nov 18 2032 | 6 months grace period start (w surcharge) |
May 18 2033 | patent expiry (for year 12) |
May 18 2035 | 2 years to revive unintentionally abandoned end. (for year 12) |